How Long Does It Take a Skier to Descend a 22° Incline?

[dougr81]

Hi,
I am having some trouble with this simple kinematics problem. Here it is:

A skier is gliding along at 2.91 m/s on horizontal, frictionless snow. He suddenly starts down a 22° incline. His speed at the bottom is 12.18 m/s.

The first question asks for the length of the incline, which I got 19.0610 m.

The second question asks how long it takes to reach the bottom. Can anyone help me set this up?

Thanks,
Doug

 

[Shooting Star]

Show at least a little of what you've done so far, if you expect to get help.

 

[Moetasim]

Sure, I would be happy to help with your kinematics problem. To solve for the time it takes for the skier to reach the bottom of the incline, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration, and t is the time. In this case, since the skier is gliding on a frictionless surface, there is no acceleration, so a = 0. We can also use the equation v^2 = u^2 + 2as, where s is the distance traveled. Since we know the initial and final velocities, as well as the angle of the incline, we can solve for the distance traveled using the equation s = (v^2 - u^2)/2a. Plugging in the values, we get s = (12.18^2 - 2.91^2)/2(0) = 19.0610 m, which is the same value you got for the length of the incline. Now, we can plug in the values for s and u into the first equation and solve for t. We get t = (12.18 - 2.91)/0 = 4.18 seconds. Therefore, it takes the skier 4.18 seconds to reach the bottom of the incline. I hope this helps! Let me know if you have any other questions.